To Shake or Not to Shake

I was in Dayton for a meeting with the client earlier this week. This guy was doing some knowledge transfer for a 3rd party user administration tool. During the meeting, I had to cough. Well, you're supposed to cover your mouth when you cough so as not to disperse your germs through the air...you know the stuff they teach you when you're a little kid and now you do without thinking about it. I had to cough, so I coughed on my right hand. I'm right-handed, so i think that makes perfect sense. But then I started thinking about it. I knew that I would probably have to shake this guy's hand after the meeting. The meeting ends, and sure enough he reaches out to shake my hand. I didn't know what to do. Do you refuse and tell him that you coughed and you don't want to offend him but you don't want to give him germs, etc., etc., etc. That seems like alot of effort. The other option is to shake his hand and hope that he wasn't baiting you because he saw you cough earlier and he can't believe that you would go ahead with the shake. It's quite the dilemma. So, I shook his hand and prayed that he didn't see the cough beforehand. If I see him again and I get the evil eye, I'll know I was busted.